Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

Ma, Shukai; Antonsen, Thomas M.; Anlage, Steven M.

doi:10.1103/physreve.106.054215

Cited by 6 publications

(6 citation statements)

References 60 publications

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“…Note that we also include the mode spacing ratio values of the GOE graph system consisting of topologically-trivial photonic crystal waveguides in the last column. [50] It is clear that a GOE graph system mode spacing ratios are at the other extreme of values, and closer to the GOE theoretical prediction values. From this mode spacing study of numerical realizations of the PTI graph system we conclude that it is more consistent with GSE statistics than any other Gaussian ensemble.…”

Section: Numerical Simulation Studiessupporting

confidence: 67%

“…The ensemble-averaged consecutive mode spacing ratios of the photonic topological insulator graph (PTI-graph) system, the theoretical predictions for the GOE, GUE, and GSE systems, [66] and the mode spacing ratios of the topologically-trivial photonic crystal graph (PC-graph). [50] PTI > 0.5), and show a distinctly different shape as compared to the GOE and GUE systems, especially in terms of the peak and tail of P(s). For small spacing values (s < 0.5), we find that the graph system deviates from the GSE class prediction.…”

Section: Numerical Simulation Studiesmentioning

confidence: 92%

“…Previous work has shown that photonic crystal defect waveguides with trivial topology can be used as quantum graphs, and display many of the same statistical properties of more conventional cable graphs. [ 50 ] The proposed PTI symplectic quantum graph structure can be considered a square pyramid realized in the 2D plane (see the inset in Figure c). Each bond of the graph is built with a QSH–QVH interface waveguide.…”

Section: Pti‐graph Designmentioning

confidence: 99%

“…We have recently demonstrated a chaotic 1D graph with topologically trivial photonic crystal defect waveguides and found good agreement with the corresponding RMT theoretical predictions. [ 50 ] . Our next step is to consider a chaotic graph structure where the BMW QSH–QVH interface waveguides realize the graph bonds, and represent the first use of topological waveguides for wave chaos studies.…”

Section: Introductionmentioning

confidence: 99%

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Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Ma,

Anlage

2023

Advanced Optical Materials

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Working in analogy with topological insulators in condensed matter, photonic topological insulators (PTI) have been experimentally realized, and protected electromagnetic edge‐modes have been demonstrated in such systems. Moreover, PTI technology also emulates a synthetic spin‐1/2 degree of freedom (DOF) in the reflectionless topological modes. The spin‐1/2 DOF is carried by quantum valley Hall (QVH)/quantum spin Hall (QSH) interface modes created from the bianisotropic meta waveguide platform and realized both in simulation and experiment. The PTI setting is employed to build an ensemble of wave chaotic 1D metric graphs that display statistical properties consistent with Gaussian symplectic ensemble (GSE) statistics. The two critical ingredients required to create a physical system in the GSE universality class, the half‐integer‐spin DOF and preserved time‐reversal invariance, are clearly realized in the QVH/QSH interface modes. The anti‐unitary T‐operator is identified for the PTI Hamiltonian underlying the experimental realization. An ensemble of PTI‐edgemode metric graphs are proposed and experimentally demonstrated. Then, the Kramers degeneracy of eigenmodes of the PTI‐graph systems is demonstrated with both numerical and experimental studies. Further, spectral statistical studies of the edgemode graphs are studied, and good agreement with the GSE theoretical predictions is found. The PTI chaotic graph structures present an innovative and easily extendable platform for continued future investigation of GSE systems.

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Section: Numerical Simulation Studiessupporting

confidence: 67%

Section: Numerical Simulation Studiesmentioning

confidence: 92%

Section: Pti‐graph Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Ma,

Anlage

2023

Advanced Optical Materials

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“…They found that the optimal control protocol is independent of the duration of nonequilibrium driving processes. The framework of thermodynamic geometry has been widely applied to solve for the optimal control protocol in many problems, such as complex nonequilibrium transitions [72], optimization of finite-time heat engines [66], and bit initialization [73]. Considering a small system far from equilibrium in a finite-rate driving process, Schmiedl and Seifert investigated the optimal control protocol with given value of final control [24].…”

mentioning

confidence: 99%

Nonequilibrium work relations meet engineered thermodynamic control: A perspective for nonequilibrium measurements

2023

EPL

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Nonequilibrium work relations establish a fundamental connection between the equilibrium properties of a system and the ﬂuctuation of work performed during nonequilibrium driving processes. However, high dissipation in fast driving processes often impedes the convergence of these work relations, complicating the accurate measurement and estimation of equilibrium properties. To address this issue, recent advances in the methodology of engineered thermodynamic control have been introduced. The goal of this method is to improve the eﬃciency of nonequilibrium measurements by engineering the driving strategies for the system. The engineered strategies enable the system to follow a desired evolution, thereby enhancing the estimation of equilibrium properties in ﬁnite-rate driving processes. In this perspective, we shed light on recent developments in this ﬁeld. Diﬀerent principles have been reviewed for engineering thermodynamic driving strategies, such as ﬁnding optimal control protocols to minimize dissipation and designing thermodynamic control protocols to shorten the lag between the system current state and its corresponding equilibrium state. Nonequilibrium measurement schemes matched with engineered thermodynamic control are also outlined as promising avenues for improving the eﬃciency and accuracy of nonequilibrium measurements, including several reﬁned nonequilibrium work relations matched with designed thermodynamic control protocols.

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Bound states in the continuum induced via local symmetries in complex structures

Wang,

Kuhl,

Dowling

et al. 2024

Phys. Rev. Applied

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Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

Cited by 6 publications

References 60 publications

Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Nonequilibrium work relations meet engineered thermodynamic control: A perspective for nonequilibrium measurements

Bound states in the continuum induced via local symmetries in complex structures

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